Cases in Marathi

In grammar, case relates noun or pronoun to the verb present in a sentence. In order to do that, noun or pronoun is distorted/inflected to match with the action of the verb.

for example

राम मारतो. (Ram kills)

रामाने मारले. (Ram killed)

रामाने रावणाला मारले. (Ram killed Ravana)

रामाने रावणाला बाणाने मारले.(Ram killed Ravana by an arrow)

The highlighted letters are called case endings that show how subject or object is altered to relate itself to the action. Indian languages including Hindi have ways of altering subjects or objects to mark roles which are not there in English. If you are a Hindi speaker, knowingly or unknowingly you are using it. Marathi case endings and Hindi case endings look very similar.

i have found some words like this-
त्यांचं,माझं,इथं,etc.
what the difference between त्यांचं[tyancha],and,त्यांचा[tyanchaa]
in which conditions do we use the word त्यांचं
the below given sentence also consists of such words.
ऋषीचं–कूळ– नदीचं–मूळ–शोधू–नये
please explain me where to use such words and in which condition.

त्यांचं[tyancha] or त्यांचे (tyanche),त्यांचा[tyanchaa] and त्यांची (tyanchi) all refers to “THEIR” in English. The difference between them depends on what follows after “THEIR”.
If the object following after “THEIR” is neither male nor female (neuter) then we use त्यांचं[tyancha] or त्यांचे (tyanche).
If the object following after “THEIR” is male then we use त्यांचा[tyanchaa].
If the object following after “THEIR” is female then we use त्यांची (tyanchi).

त्यांच झाड or त्यांचे झाड means Their tree (neuter)
त्यांचा मुलगा means their son (male)
त्यांची शाळा means their school (although school is neuter in English it is female in Marathi)
त्यांची मुलगी means their daughter (female)